Equivalence of viscosity and weak solutions for a p-parabolic equation

被引：7

作者：

Siltakoski, Jarkko ^{[1
]}

机构：

[1] Univ Jyvaskyla, Dept Math & Stat, POB 35, Jyvaskyla 40014, Finland

来源：

JOURNAL OF EVOLUTION EQUATIONS | 2021年 / 21卷 / 02期

关键词：

Comparison principle; Gradient term; Parabolic p-Laplacian; Viscosity solution; Weak solution; SUPERSOLUTIONS; REGULARITY; BOUNDARY; MAXIMUM;

D O I：

10.1007/s00028-020-00666-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the relationship of viscosity and weak solutions to the equation partial derivative(t)u - Delta(p)u = f (Du), where p > 1 and f is an element of C(R-N) satisfies suitable assumptions. Our main result is that bounded viscosity supersolutions coincide with bounded lower semicontinuous weak supersolutions. Moreover, we prove the lower semicontinuity of weak supersolutions when p >= 2.

引用

页码：2047 / 2080

页数：34

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